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Let \(f(x)\) be a function such that \(f(x)=|x^2-4|-1\) and \(g(x)\) a function such that \(g(x)=\sqrt{f(x)}\). The domain of \(g(x)\) can be written as \((-\infty,-\sqrt{a}] \cup [-\sqrt{b},\sqrt{c}] \cup [\sqrt{d},+\infty)\). Find the value of \(a+b+c+d\)